Sensitivity analysis in functional principal component analysis

Yoshihiro Yamanishi, Yutaka Tanaka

    研究成果: ジャーナルへの寄稿記事

    9 引用 (Scopus)

    抄録

    In the present paper empirical influence functions (EIFs) are derived for eigenvalues and eigenfunctions in functional principal component analysis in both cases where the smoothing parameter is fixed and unfixed. Based on the derived influence functions a sensitivity analysis procedure is proposed for detecting jointly as well as singly influential observations. A numerical example is given to show the usefulness of the proposed procedure. In dealing with the influence on the eigenfunctions two different kinds of influence statistics are introduced. One is based on the EIF for the coefficient vectors of the basis function expansion, and the other is based on the sampled vectors of the functional EIF. Under a certain condition it can be proved both kinds of statistics provide essentially equivalent results.

    元の言語英語
    ページ(範囲)311-326
    ページ数16
    ジャーナルComputational Statistics
    20
    発行部数2
    DOI
    出版物ステータス出版済み - 12 1 2005

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    Functional Principal Component Analysis
    Influence Function
    Principal component analysis
    Sensitivity analysis
    Sensitivity Analysis
    Eigenvalues and eigenfunctions
    Statistics
    Influential Observations
    Eigenvalues and Eigenfunctions
    Smoothing Parameter
    Eigenfunctions
    Basis Functions
    Numerical Examples
    Influence function
    Coefficient
    Influence

    All Science Journal Classification (ASJC) codes

    • Statistics and Probability
    • Statistics, Probability and Uncertainty
    • Computational Mathematics

    これを引用

    Sensitivity analysis in functional principal component analysis. / Yamanishi, Yoshihiro; Tanaka, Yutaka.

    :: Computational Statistics, 巻 20, 番号 2, 01.12.2005, p. 311-326.

    研究成果: ジャーナルへの寄稿記事

    Yamanishi, Yoshihiro ; Tanaka, Yutaka. / Sensitivity analysis in functional principal component analysis. :: Computational Statistics. 2005 ; 巻 20, 番号 2. pp. 311-326.
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